Theorem in2an

Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd is the non-virtual deduction form of in2an . (Contributed by Alan Sare, 30-Jun-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	in2an.1	$$⊢\left(\phi ,\left(\psi \wedge \chi \right)\to \theta \right)$$
Assertion	in2an	$$⊢\left(\phi ,\psi \to \left(\chi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		in2an.1	$$⊢\left(\phi ,\left(\psi \wedge \chi \right)\to \theta \right)$$
2	1	dfvd2i	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	2	expd	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
4	3	dfvd2ir	$$⊢\left(\phi ,\psi \to \left(\chi \to \theta \right)\right)$$